Abstract
In this paper, we apply the Adomian decomposition method combined with the Laplace transform (LADM) in order to solve the cubic nonlinear Schrödinger equation for special cases Akhmediev breather (AB), Peregrine (PS) and Kuznetsov-Ma (KM) solitons. The proposed iterative scheme finds the solution without the need for a linearization or discretization process. Finally, five numerical examples are given to verify the high accuracy and reliability of the proposed analytical approach.
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